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Olson Order of Quantum Observables

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Abstract

M.P. Olson, Proc. Am. Math. Soc. 28, 537–544 (1971) showed that the system of effect operators of the Hilbert space can be ordered by the so-called spectral order such that the system of effect operators is a complete lattice. Using his ideas, we introduce a partial order, called the Olson order, on the set of bounded observables of a complete lattice effect algebra. We show that the set of bounded observables is a Dedekind complete lattice.

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Acknowledgments

The author is very indebted to an anonymous referee for his/her careful reading and suggestions which helped us to improve the readability of the paper.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Department Algebra Geometry, Palacký University, 17. listopadu 12, CZ-771 46, Olomouc, Czech Republic

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Correspondence to Anatolij Dvurečenskij.

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The paper has been supported by the grant VEGA No. 2/0069/16 SAV and GAČR 15-15286S.

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Dvurečenskij, A. Olson Order of Quantum Observables. Int J Theor Phys 55, 4896–4912 (2016). https://doi.org/10.1007/s10773-016-3113-9

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  • DOI: https://doi.org/10.1007/s10773-016-3113-9

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